Question: Simplify. Remove all perfect squares from inside the square root. Assume $y$ is positive. $\sqrt{39y^9}=$
Factor $39$ and find the greatest perfect square: $39=3 \cdot 13$ There are no perfect squares in $39$. Find the greatest perfect square in $y^9$ : $y^9=\left(y^4\right)^2\cdot y$ $\begin{aligned} \sqrt{39y^9}&=\sqrt{39\cdot \left(y^4\right)^2\cdot y} \\\\ &= \sqrt{39} \cdot \sqrt{\left(y^4\right)^2}\cdot \sqrt{y} \\\\ &= \sqrt{39} \cdot y^4\cdot \sqrt{y} \\\\ &=y^4\sqrt{39y} \end{aligned}$